Poiseuille Number Correlations for Gas Slip Flow in Micro-Tubes

Abstract

Fundamental research in fluid flow characteristics in micro-tubes are required for designing microfluidic systems. In this study, Poiseuille number, the product of friction factor and Reynolds number (f · Re) for quasi-fully developed micro-tube flows, was obtained for slip flow regime. The numerical methodology was based on the Arbitrary-Lagrangian-Eulerian (ALE) method and the uncertainties of the results were assessed based on the grid convergence index (GCI). The numerical model was validated with the available experimental and numerical results. The compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers with two thermal boundary conditions: constant wall temperature (CWT), and constant heat flux (CHF), respectively. The slip boundary conditions and their numerical implementation are appropriately documented. The tube diameter ranged from 3 to 10 μm and the tube aspect ratio was 200. The stagnation pressure was chosen in such a way that the exit Mach number ranged from 0.1–1.0. The outlet pressure was fixed at the atmospheric condition. It was found that for the case of compressible and slip flows, f · Re correlations are functions of the Mach and Knudsen numbers, and are different from the values obtained from the expression, 64/(1 + 8 Kn), available for the incompressible slip flow regime. The f · Re correlations obtained here are applicable to both no-slip and slip conditions, and for both incompressible and compressible flows. The results are in excellent agreement with the available experimental data.

Financial support from the Japan Society for the Promotion of Science (Grant-in-aid for Scientific Research (C) #16560189) is greatly acknowledged.